This is an excellent question, however I think water is the outlier. The alcohols seem to me to follow a predictable pattern. Water (or hydrogen) seems to not follow that pattern.
If you compare the acidity of protonated dimethyl ether (-3.8 ) with protonated THF (-2.1), this seems consistent with methanol (15.5), ethanol (16), isopropanol (16.5), and t-butanol (17). If methyl groups are replaced with hydrogen, the protonated methanol (-2.2) and hydronium (-1.7) seem to have a trend counter to the electron donation of substituted carbons. In virtually all other circumstances, carbon is a better electron donor than hydrogen.
I agree with the suggestion of movies to consider the gas phase acidities in which the acidities do follow the predicted trend. I am wary of gas phase acidities (probably because I do not understand them). However, I do think that we can learn from the gas phase acidities as to how they might differ from solution pKa values in that solvent effects are removed. If I accept this consequence to the measurement of pKa values, then I would contemplate whether hydrogen bonding might reverse the electron withdrawing properties of protons. If pKa measurements are solvent dominated, that is only a small amount of acids are present, then we could consider the bulk hydrogen bonding present could stretch the O-H bonds and make the non-bonded electrons of oxygen more available. This would be an effect opposite of a proton being an electron withdrawing group, but consistent with hydrogen bonding.